Determine the intervals on which the function is concave up or down and find the points of inflection. \[ f(x)=8 x^{3}-5 x^{2}+6 \] (Give your answer as a comma-separated list of points in the form $(*, *$ ). Express numbers in exact form. Use notation and fractions where needed.)

Step 1 ：First, we find the first derivative of the function, which is \(f'(x) = 24x^2 - 10x\).

Step 2 ：Next, we find the second derivative of the function, which is \(f''(x) = 48x - 10\).

Step 3 ：To find the points of inflection, we set the second derivative equal to zero and solve for x: \(48x - 10 = 0\), which simplifies to \(x = 5/24\).

Step 4 ：We then test the intervals around the point of inflection in the second derivative. For \(x < 5/24\), we use \(x = 0\) and find that \(f''(0) = -10\), which is less than 0. Therefore, the function is concave down on the interval \((-∞, 5/24)\).

Step 5 ：For \(x > 5/24\), we use \(x = 1\) and find that \(f''(1) = 38\), which is greater than 0. Therefore, the function is concave up on the interval \((5/24, ∞)\).

Step 6 ：Finally, we find that the point of inflection is at \((5/24, f(5/24)) = (5/24, 8*(5/24)^3 - 5*(5/24)^2 + 6)\).

Step 7 ：\(\boxed{\text{Therefore, the function is concave down on } (-∞, 5/24) \text{ and concave up on } (5/24, ∞). \text{ The point of inflection is at } (5/24, f(5/24)) = (5/24, 8*(5/24)^3 - 5*(5/24)^2 + 6)}\)